Rooted edges of a minimal directed spanning tree on random points

Z. D. Bai, Sungchul Lee, Mathew D. Penrose

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

For n independent, identically distributed uniform points in [0, 1]d, d ≥ 2, let Ln be the total distance from the origin to all the minimal points under the coordinatewise partial order (this is also the total length of the rooted edges of a minimal directed spanning tree on the given random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of Ln, and show that Ln satisfies a central limit theorem, unlike in the case d = 2.

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalAdvances in Applied Probability
Volume38
Issue number1
DOIs
Publication statusPublished - 2006 Mar 1

Fingerprint

Spanning tree
Partial Order
Central limit theorem
Identically distributed

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

Cite this

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Rooted edges of a minimal directed spanning tree on random points. / Bai, Z. D.; Lee, Sungchul; Penrose, Mathew D.

In: Advances in Applied Probability, Vol. 38, No. 1, 01.03.2006, p. 1-30.

Research output: Contribution to journalArticle

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